Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
16.5-a1
16.5-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( 2^{11} \)
$0.73687$
$(-a-1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$18.47046131$
0.559968109
\( -343 a + 1029 \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$
16.5-a2
16.5-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( - 2^{10} \)
$0.73687$
$(-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$4.617615327$
0.559968109
\( -2701312025 a + 6919553753 \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 7 a - 2\) , \( 5 a - 5\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(7a-2\right){x}+5a-5$
16.5-a3
16.5-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( 2^{8} \)
$0.73687$
$(-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$18.47046131$
0.559968109
\( -24225 a + 68453 \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a+3\right){x}$
16.5-a4
16.5-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( 2^{10} \)
$0.73687$
$(-a-1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$36.94092262$
0.559968109
\( 1995 a + 5021 \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 12 a - 22\) , \( -7 a + 26\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-22\right){x}-7a+26$
16.5-a5
16.5-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( - 2^{4} \)
$0.73687$
$(-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$9.235230655$
0.559968109
\( 7659605 a + 11960871 \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 4\) , \( 5 a - 16\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-4\right){x}+5a-16$
16.5-a6
16.5-a
$6$
$8$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( 2^{11} \)
$0.73687$
$(-a-1)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$36.94092262$
0.559968109
\( 21069823 a + 33751811 \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 127 a - 317\) , \( -1109 a + 2848\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a-317\right){x}-1109a+2848$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.